Differential and Integral Calculus Summer 25 - MID

Daffodil International University Department of Business Administration Course Title: Differentiation and Integral Calculus Course Code: 0541-214 Semester: Summer 2025 Time: 1 Hour 30 minutes Section: All Examination: Midterm Full Marks: 25 Teachers' Initial: MP, DMSA, AA, ARE, Jl 01 02 03 04 a) b) a) b) c) a) b) a) b) c) DB : Answer all the following questions] Discuss the price elasticity of demand with examples. Distinguish between relation and fimction_ Solve the domain and range ofthe åmction y Sketch the graph of the function y = x2 — 2 Solve for limiting value of lim Examine Y' 4x3 + 2 x z + I ox + 40 ii_ y (x + 1) (x 2 After x weeks, the number of people using a new rapid transit system was approximately N(x) = 4x3 + 30x + 3500. Apply the rules of differentiation to find at what rate was the use of the system changing with respect to time aner 4 weeks A manufacturer estimates that when x units of a particular commodity are produced, the total cost will be C(x) = 0.2x2 + 4x + 57 dollars, and fiurthermore that all x units will be sold when the price is p (x) - (36 — x) dollars per unit Develop the marginal cost and the marginal revenue åunction Apply the marginal cost function to estimate the cost of producing the ninth unit Identiör the actual cost of producing the ninth unit. (CLO 2, L2) (CLO 4, L4) (CLO 3: L3) (CLO 3: L3) (CLO 3: L3) (CLO 3: L3) (CLO 3: L3) (CLO 3: L3) 2 1.5 1.5 2 3 15 15 2 3 2 05 a) b) A book publisher estimates that when q thousand copies of a book are printed each month: the total cost will be C (q) = 2.5q2 + 4q + 60 thousand dollars: and the selling price per book is given by p(q) = 36 — 1.5q dollars per copy. Determine the number of units that results in maximum profit. Identiör the value of the maximum profit. (CLO 3: L3) (CLO 3: L3) 2